3,628,800
3,628,800 is 10 factorial — the number of ways to order ten items.
- Even
- Composite
Where 3,628,800 fits
Why 3,628,800 is special
Ten things can be arranged in over three and a half million ways, which is the point at which arranging by hand stops being possible. The jump from 9! to 10! adds three million orderings on its own, and the sequence keeps accelerating from there.
Factors & digit properties
- Divisors (270)
- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 200, 210, 216, 224, 225, 240, 252, 256, 270, 280, 288, 300, 315, 320, 324, 336, 350, 360, 378, 384, 400, 405, 420, 432, 448, 450, 480, 504, 525, 540, 560, 567, 576, 600, 630, 640, 648, 672, 675, 700, 720, 756, 768, 800, 810, 840, 864, 896, 900, 945, 960, 1008, 1050, 1080, 1120, 1134, 1152, 1200, 1260, 1280, 1296, 1344, 1350, 1400, 1440, 1512, 1575, 1600, 1620, 1680, 1728, 1792, 1800, 1890, 1920, 2016, 2025, 2100, 2160, 2240, 2268, 2304, 2400, 2520, 2592, 2688, 2700, 2800, 2835, 2880, 3024, 3150, 3200, 3240, 3360, 3456, 3600, 3780, 3840, 4032, 4050, 4200, 4320, 4480, 4536, 4725, 4800, 5040, 5184, 5376, 5400, 5600, 5670, 5760, 6048, 6300, 6400, 6480, 6720, 6912, 7200, 7560, 8064, 8100, 8400, 8640, 8960, 9072, 9450, 9600, 10080, 10368, 10800, 11200, 11340, 11520, 12096, 12600, 12960, 13440, 14175, 14400, 15120, 16128, 16200, 16800, 17280, 18144, 18900, 19200, 20160, 20736, 21600, 22400, 22680, 24192, 25200, 25920, 26880, 28350, 28800, 30240, 32400, 33600, 34560, 36288, 37800, 40320, 43200, 44800, 45360, 48384, 50400, 51840, 56700, 57600, 60480, 64800, 67200, 72576, 75600, 80640, 86400, 90720, 100800, 103680, 113400, 120960, 129600, 134400, 145152, 151200, 172800, 181440, 201600, 226800, 241920, 259200, 302400, 362880, 403200, 453600, 518400, 604800, 725760, 907200, 1209600, 1814400, 3628800
- Prime factorisation
- 2^8 × 3^4 × 5^2 × 7
- Digit sum
- 27
- Digital root
- 9
Representations
- Decimal
- 3628800
- Scientific notation
- 3.629 × 10^6
Roman numerals
Roman numerals as modelled here goes up to 3,999.
Binary
1 1 0 1 1 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0
1 × 2,097,152 + 1 × 1,048,576 + 0 × 524,288 + 1 × 262,144 + 1 × 131,072 + 1 × 65,536 + 0 × 32,768 + 1 × 16,384 + 0 × 8,192 + 1 × 4,096 + 1 × 2,048 + 1 × 1,024 + 1 × 512 + 1 × 256 + 0 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 3,628,800
Octal
1 5 6 5 7 4 0 0
1 × 2,097,152 + 5 × 262,144 + 6 × 32,768 + 5 × 4,096 + 7 × 512 + 4 × 64 + 0 × 8 + 0 × 1 = 3,628,800
Hexadecimal
3 7 5 f 0 0
3 × 1,048,576 + 7 × 65,536 + 5 × 4,096 + f × 256 + 0 × 16 + 0 × 1 = 3,628,800
In historical numeral systems
Egyptian
3 Heh figures, 6 tadpoles, 2 fingers, 8 lotuses, 8 coils of rope
3 × 1,000,000 + 6 × 100,000 + 2 × 10,000 + 8 × 1,000 + 8 × 100 = 3,628,800. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Factorial number
- Harshad (Niven) number
Related numbers & connections
10! is ten times 9!. Each step multiplies by the next integer, which is why the sequence outruns anything polynomial almost immediately.
View 362880 →Mathematically related
- is a multiple of362880
why?
Strength 0.50, confidence "high".
Mathematics
Ten items have 3,628,800 arrangements. The step from nine items to ten adds more than three million orderings by itself, which is the practical reason so much of computer science is about avoiding enumeration rather than speeding it up.
DocumentedMathematics
Common questions
Is 3,628,800 a prime number?
No, 3,628,800 is not prime.
What are the factors of 3,628,800?
The factors of 3,628,800 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 200, 210, 216, 224, 225, 240, 252, 256, 270, 280, 288, 300, 315, 320, 324, 336, 350, 360, 378, 384, 400, 405, 420, 432, 448, 450, 480, 504, 525, 540, 560, 567, 576, 600, 630, 640, 648, 672, 675, 700, 720, 756, 768, 800, 810, 840, 864, 896, 900, 945, 960, 1008, 1050, 1080, 1120, 1134, 1152, 1200, 1260, 1280, 1296, 1344, 1350, 1400, 1440, 1512, 1575, 1600, 1620, 1680, 1728, 1792, 1800, 1890, 1920, 2016, 2025, 2100, 2160, 2240, 2268, 2304, 2400, 2520, 2592, 2688, 2700, 2800, 2835, 2880, 3024, 3150, 3200, 3240, 3360, 3456, 3600, 3780, 3840, 4032, 4050, 4200, 4320, 4480, 4536, 4725, 4800, 5040, 5184, 5376, 5400, 5600, 5670, 5760, 6048, 6300, 6400, 6480, 6720, 6912, 7200, 7560, 8064, 8100, 8400, 8640, 8960, 9072, 9450, 9600, 10080, 10368, 10800, 11200, 11340, 11520, 12096, 12600, 12960, 13440, 14175, 14400, 15120, 16128, 16200, 16800, 17280, 18144, 18900, 19200, 20160, 20736, 21600, 22400, 22680, 24192, 25200, 25920, 26880, 28350, 28800, 30240, 32400, 33600, 34560, 36288, 37800, 40320, 43200, 44800, 45360, 48384, 50400, 51840, 56700, 57600, 60480, 64800, 67200, 72576, 75600, 80640, 86400, 90720, 100800, 103680, 113400, 120960, 129600, 134400, 145152, 151200, 172800, 181440, 201600, 226800, 241920, 259200, 302400, 362880, 403200, 453600, 518400, 604800, 725760, 907200, 1209600, 1814400, 3628800.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026